Slice sampling with adaptive multivariate steps: The shrinking-rank method

Madeleine Thompson, Dept. of Statistics, University of Toronto
Radford M. Neal, Dept. of Statistics and Dept. of Computer Science, University of Toronto

The shrinking rank method is a variation of slice sampling that is efficient at sampling from mul- tivariate distributions with highly correlated parameters. It requires that the gradient of the log- density be computable. At each individual step, it approximates the current slice with a Gaussian occupying a shrinking-dimension subspace. The dimension of the approximation is shrunk orthogo- nally to the gradient at rejected proposals, since the gradients at points outside the current slice tend to point towards the slice. This causes the proposal distribution to converge rapidly to an estimate of the longest axis of the slice, resulting in states that are less correlated than those generated by related methods. After describing the method, we compare it to two other methods on several distributions and obtain favorable results.

JSM 2010, Section on Statistical Computing, pp. 3890-3896:: pdf.

Associated references: The following technical report is related to the conference paper above:
Thompson, M. and Neal, R. M. (2010) ``Covariance-adaptive slice sampling'', Technical Report No. 1002, Dept. of Statistics, University of Toronto, 17 pages: abstract, postscript, pdf.